Subgroups — #14419071

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#713	C₂	1	1	yes	maximal, characteristic
2	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747013	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747010	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747003	C₂	1	2	yes	maximal, complemented
7	#11746997	C₂	1	2	yes	maximal, complemented
8	#11746991	C₂	1	2	yes	maximal, complemented
9	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746869	C₂	1	2	yes	maximal, complemented
11	#11746869	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611669	—	3	1	no	maximal, Hall
13	C₂×C₃×#713	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic
16	C₃×#4039	C₄	1	2	yes	—
17	C₃×#4039	C₄	1	1	yes	characteristic
18	C₃×#4038	C₄	1	2	yes	—
19	C₃×#4038	C₄	1	1	yes	characteristic
20	C₃×C₄×D₂₀	C₂²	1	2	yes	—
21	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₄²×D₅	C₂²	1	2	yes	—
24	C₂×#6649	C₂²	1	2	yes	—
25	C₂×#6649	C₂²	1	2	yes	—
26	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
29	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
30	#91087	C₂²	1	2	yes	—
31	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
32	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₅×#803	C₂²	1	2	yes	—
35	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	#90955	C₂²	1	2	yes	—
37	#90955	C₂²	1	2	yes	—
38	#90955	C₂²	1	2	yes	—
39	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
40	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
41	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#82517	—	5	1	no	maximal, Hall
43	C₄×#713	D₃	1	1	yes	characteristic
44	C₅×#446	—	3	1	no	—
45	#65313	—	3	1	no	—
46	#65127	—	3	1	no	—
47	#65125	—	3	2	no	—
48	#65122	—	3	1	no	—
49	#65122	—	3	2	no	—
50	#64996	—	3	2	no	—
51	#64995	—	3	2	no	—
52	#64977	—	3	1	no	—
53	C₄×C₈×D₅	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₃×#713	—	2	4	no	—
56	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
57	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₃×#685	C₂×C₄	1	2	yes	—
75	C₃×#685	C₂×C₄	1	2	yes	—
76	C₃×#685	C₂×C₄	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	#6649	—	2	4	no	—
85	#6649	—	2	4	no	—
86	D₅×C₃⋊C₈	—	2	2	no	—
87	D₅×C₃⋊C₈	—	2	2	no	—
88	C₃×C₄×#41	—	5	1	no	—
89	#5024	—	5	1	no	—
90	#5024	D₅	1	1	yes	characteristic, complemented
91	#5012	—	5	1	no	—
92	#5012	—	5	1	no	—
93	#5011	—	5	2	no	—
94	#5011	—	5	2	no	—
95	#4925	—	5	2	no	—
96	#4925	—	5	1	no	—
97	C₄×#208	—	5	2	no	—
98	C₂×C₄×C₃⋊C₈	—	5	1	no	—
99	C₂×#713	Dic₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
101	Q₈×Dic₅	Dic₃	1	1	yes	characteristic
102	C₂×#676	—	3	2	no	—
103	C₂×#676	—	3	2	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	C₂×C₈×D₅	—	3	1	no	—
106	#4039	Dic₃	1	2	yes	—
107	#4039	Dic₃	1	1	yes	characteristic
108	#4038	Dic₃	1	2	yes	—
109	#4038	Dic₃	1	1	yes	characteristic
110	C₄×D₂₀	C₂×D₃	1	2	yes	—
111	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
112	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
113	C₄²×D₅	C₂×D₃	1	2	yes	—
114	C₅×C₄⋊C₈	—	3	2	no	—
115	C₅×C₄⋊C₈	—	3	1	no	—
116	C₅×#97	—	3	2	no	—
117	C₄×C₅×C₈	—	3	1	no	—
118	#3952	—	3	2	no	—
119	#3952	—	3	2	no	—
120	#3952	—	3	2	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	—	3	1	no	—
124	C₄⋊#168	—	3	1	no	—
125	C₄⋊#168	—	3	2	no	—
126	#3935	—	3	2	no	—
127	C₄×#168	—	3	1	no	—
128	#2965	—	15	1	no	Sylow
129	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
130	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
141	C₃×D₂₀	—	2	4	no	—
142	C₃×D₂₀	—	2	2	no	—
143	C₃×C₄×D₅	—	2	1	no	—
144	C₃×C₄×D₅	—	2	1	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	—	2	4	no	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	—	2	4	no	—
150	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	—	2	2	no	—
153	C₃⋊#168	#41	1	2	yes	complemented
154	C₅×C₃⋊C₈	—	2	1	no	—
155	C₅×C₃⋊C₈	—	2	2	no	—
156	C₅×C₃⋊C₈	#41	1	2	yes	complemented
157	C₂×C₃×#41	—	5	1	no	—
158	C₃×C₄×Q₈	—	5	1	no	—
159	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
160	C₃×C₄×D₄	—	5	2	no	—
161	C₃×C₄×D₄	—	5	1	no	—
162	C₃×C₄×D₄	—	5	2	no	—
163	C₃×C₄×D₄	—	5	1	no	—
164	C₃×#117	—	5	1	no	—
165	C₃×#117	—	5	2	no	—
166	C₂×C₃×C₄²	—	5	1	no	—
167	C₂×C₃×C₄²	—	5	2	no	—
168	C₂×#208	—	5	2	no	—
169	C₂×#208	—	5	2	no	—
170	C₂²×C₃⋊C₈	—	5	1	no	—
171	C₂²×C₃⋊C₈	—	5	1	no	—
172	#830	—	5	2	no	—
173	#830	—	5	2	no	—
174	#830	—	5	2	no	—
175	C₄⋊(C₃⋊C₈)	—	5	2	no	—
176	C₄⋊(C₃⋊C₈)	—	5	1	no	—
177	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
178	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
179	#803	—	5	2	no	—
180	#803	C₂×D₅	1	2	yes	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₄×C₃⋊C₈	—	5	1	no	—
184	C₄×C₃⋊C₈	—	5	2	no	—
185	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
186	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
187	#713	—	2	4	no	—
188	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
189	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
190	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
191	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
192	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
193	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
194	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	—	3	2	no	—
199	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
200	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₄²×C₅	C₂²×D₃	1	2	yes	—
203	#685	C₂×Dic₃	1	2	yes	—
204	#685	C₂×Dic₃	1	2	yes	—
205	#685	C₂×Dic₃	1	2	yes	—
206	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
207	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
208	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
209	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
210	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
211	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
212	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	3	1	no	—
215	C₂×#168	—	3	2	no	—
216	#676	—	6	4	no	—
217	#676	—	6	4	no	—
218	C₈×D₅	—	6	2	no	—
219	C₈×D₅	—	6	2	no	—
220	C₄×#41	—	5	1	no	—
221	#446	—	3	1	no	—
222	#446	—	15	1	no	—
223	#436	—	15	1	no	—
224	#436	—	15	1	no	—
225	#435	—	15	2	no	—
226	#435	—	15	2	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₄×M₁₆	—	15	2	no	—
230	C₂×C₄×C₈	—	15	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₃×D₅	—	2	1	no	—
233	C₂×C₃×D₅	—	2	1	no	—
234	C₂×C₃×D₅	—	2	2	no	—
235	C₂×C₃×D₅	—	2	2	no	—
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₃×Dic₅	—	2	1	no	—
245	C₃×Dic₅	—	2	2	no	—
246	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
247	C₃×Dic₅	#131	1	2	yes	—
248	C₃×#41	—	10	4	no	—
249	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
250	C₂×C₃×D₄	—	5	2	no	—
251	C₂×C₃×D₄	—	5	1	no	—
252	C₂²×C₃×C₄	—	5	1	no	—
253	C₂²×C₃×C₄	—	5	2	no	—
254	C₂²×C₃×C₄	—	5	1	no	—
255	C₂²×C₃×C₄	—	5	2	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	5	2	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
261	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
262	C₃×C₂²⋊C₄	—	5	2	no	—
263	C₃×C₂²⋊C₄	—	5	2	no	—
264	C₃×C₂²⋊C₄	—	5	2	no	—
265	C₃×C₄²	—	5	1	no	—
266	C₃×C₄²	—	5	2	no	—
267	C₃×C₄²	—	5	2	no	—
268	C₃×C₄²	—	5	1	no	—
269	C₃×C₄²	—	5	1	no	—
270	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
271	C₃×C₄²	C₂²×D₅	1	2	yes	—
272	#208	—	10	4	no	—
273	#208	—	10	4	no	—
274	C₂×C₃⋊C₈	—	5	1	no	—
275	C₂×C₃⋊C₈	—	5	1	no	—
276	C₂×C₃⋊C₈	—	5	2	no	—
277	C₂×C₃⋊C₈	—	10	2	no	—
278	C₂×C₃⋊C₈	—	10	2	no	—
279	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
280	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
281	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
282	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
283	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
284	C₅×Q₈	—	2	2	no	—
285	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
286	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
288	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
290	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
291	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
292	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
293	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
294	D₂₀	—	2	4	no	—
295	D₂₀	—	2	2	no	—
296	C₄×D₅	—	2	1	no	—
297	C₄×D₅	—	2	1	no	—
298	C₄×D₅	—	2	2	no	—
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	4	no	—
301	C₄×D₅	—	2	2	no	—
302	C₄×D₅	—	2	4	no	—
303	C₄×D₅	#208	1	4	yes	complemented
304	C₅×C₈	—	3	2	no	—
305	C₅×C₈	—	6	1	no	—
306	C₅×C₈	—	6	2	no	—
307	#168	—	3	2	no	—
308	#168	—	6	1	no	—
309	#168	—	6	2	no	—
310	C₂×#41	—	5	1	no	—
311	C₂×M₁₆	—	15	2	no	—
312	C₂×M₁₆	—	15	2	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	—	15	1	no	—
315	C₄×Q₈	—	5	1	no	—
316	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
317	C₄×D₄	—	5	2	no	—
318	C₄×D₄	—	5	1	no	—
319	C₄×D₄	—	5	2	no	—
320	C₄×D₄	—	5	1	no	—
321	#117	—	5	1	no	—
322	#117	—	5	2	no	—
323	C₂×C₄²	—	5	1	no	—
324	C₂×C₄²	—	5	2	no	—
325	C₄⋊C₈	—	3	2	no	—
326	C₄⋊C₈	—	3	1	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	—	15	1	no	—
329	C₂²⋊C₈	—	15	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	#97	—	3	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	3	1	no	—
335	C₄×C₈	—	15	1	no	—
336	C₄×C₈	—	15	1	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	—	15	1	no	—
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	C₃×D₅	—	2	2	no	—
343	C₃×D₅	—	4	2	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂³×C₃	—	5	2	no	—
346	C₃×Q₈	—	2	2	no	—
347	C₃×D₄	—	10	4	no	—
348	C₃×D₄	—	10	2	no	—
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	5	1	no	—
351	C₂×C₃×C₄	—	5	4	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	5	2	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	—	10	4	no	—
356	C₂×C₃×C₄	—	10	4	no	—
357	C₂×C₃×C₄	—	10	1	no	—
358	C₂×C₃×C₄	—	10	2	no	—
359	C₂×C₃×C₄	—	10	1	no	—
360	C₂×C₃×C₄	—	10	2	no	—
361	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
363	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
366	C₃⋊C₈	—	2	1	no	—
367	C₃⋊C₈	—	2	2	no	—
368	C₃⋊C₈	—	5	2	no	—
369	C₃⋊C₈	—	10	1	no	—
370	C₃⋊C₈	—	10	2	no	—
371	C₃⋊C₈	#713	1	2	yes	complemented
372	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
373	C₂×D₅	—	2	1	no	—
374	C₂×D₅	—	2	1	no	—
375	C₂×D₅	—	2	2	no	—
376	C₂×D₅	—	2	2	no	—
377	C₂×D₅	—	2	2	no	—
378	C₂×D₅	C₂×#208	1	2	yes	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	C₂×#208	1	2	yes	—
383	C₄×C₅	D₃×#41	1	1	yes	characteristic
384	C₄×C₅	D₃×#41	1	1	yes	characteristic
385	Dic₅	—	2	1	no	—
386	Dic₅	—	2	2	no	—
387	Dic₅	C₂×#208	1	2	yes	—
388	Dic₅	#948	1	2	yes	—
389	#41	—	10	4	no	—
390	C₂×Q₈	D₅×Dic₃	1	1	yes	characteristic
391	C₂×D₄	—	5	2	no	—
392	C₂×D₄	—	5	1	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	2	no	—
395	C₂²×C₄	—	5	1	no	—
396	C₂²×C₄	—	5	2	no	—
397	C₂²×C₄	—	5	1	no	—
398	C₂²×C₄	—	5	2	no	—
399	M₁₆	—	30	4	no	—
400	M₁₆	—	30	4	no	—
401	C₂×C₈	—	3	1	no	—
402	C₂×C₈	—	3	1	no	—
403	C₂×C₈	—	3	2	no	—
404	C₂×C₈	—	15	1	no	—
405	C₂×C₈	—	15	1	no	—
406	C₂×C₈	—	15	2	no	—
407	C₂×C₈	—	30	2	no	—
408	C₂×C₈	—	30	2	no	—
409	C₄⋊C₄	—	5	2	no	—
410	C₄⋊C₄	—	5	1	no	—
411	C₄⋊C₄	D₅×Dic₃	1	2	yes	—
412	C₄⋊C₄	D₅×Dic₃	1	1	yes	characteristic
413	C₂²⋊C₄	—	5	2	no	—
414	C₂²⋊C₄	—	5	2	no	—
415	C₂²⋊C₄	—	5	2	no	—
416	C₄²	—	5	1	no	—
417	C₄²	—	5	2	no	—
418	C₄²	—	5	2	no	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
422	C₄²	C₂×D₃×D₅	1	2	yes	—
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	2	no	—
425	C₂²×C₃	—	10	1	no	—
426	C₂²×C₃	—	10	1	no	—
427	C₂²×C₃	—	10	2	no	—
428	C₂²×C₃	—	10	2	no	—
429	C₂²×C₃	—	10	2	no	—
430	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	5	2	no	—
435	C₃×C₄	—	5	2	no	—
436	C₃×C₄	—	10	1	no	—
437	C₃×C₄	—	10	2	no	—
438	C₃×C₄	D₅×M₁₆	1	2	yes	—
439	C₃×C₄	C₂×#713	1	1	yes	characteristic
440	C₃×C₄	D₅×#41	1	1	yes	characteristic
441	C₂×C₅	C₂²×#208	1	1	yes	characteristic
442	C₂×C₅	C₂×#948	1	1	yes	characteristic
443	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
444	D₅	—	2	2	no	—
445	D₅	—	4	2	no	—
446	C₂³	—	5	1	no	—
447	C₂³	—	5	2	no	—
448	Q₈	—	2	2	no	—
449	D₄	—	10	4	no	—
450	D₄	—	10	2	no	—
451	C₂×C₄	—	5	1	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	5	4	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	10	4	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	4	no	—
459	C₂×C₄	—	10	1	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	10	1	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
464	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
465	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
466	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	3	2	no	—
469	C₈	—	6	1	no	—
470	C₈	—	6	2	no	—
471	C₈	—	15	2	no	—
472	C₈	—	30	1	no	—
473	C₈	—	30	2	no	—
474	C₂×C₃	—	10	2	no	—
475	C₂×C₃	—	20	2	no	—
476	C₂×C₃	C₄×#713	1	1	yes	characteristic
477	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
478	C₂×C₃	D₅×#131	1	1	yes	characteristic
479	C₅	#82517	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	5	2	no	—
481	C₂²	—	10	1	no	—
482	C₂²	—	10	1	no	—
483	C₂²	—	10	2	no	—
484	C₂²	—	10	2	no	—
485	C₂²	—	10	2	no	—
486	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	5	2	no	—
491	C₄	—	5	2	no	—
492	C₄	—	10	1	no	—
493	C₄	—	10	2	no	—
494	C₄	D₅×#208	1	2	yes	—
495	C₄	D₃×#713	1	1	yes	characteristic
496	C₄	#92034	1	1	yes	characteristic
497	C₃	#10611669	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	10	2	no	—
499	C₂	—	20	2	no	—
500	C₂	C₂×D₅×#208	1	1	yes	characteristic
501	C₂	Dic₃×#713	1	1	yes	characteristic
502	C₂	D₅×#948	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×Q₈	C₂²
prime radical	C₂×C₃×#713	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #11751125	C₂	semidirect
3. C₅×#5024	C₂	semidirect
4. #11747013	C₂	semidirect
5. #11747010	C₂	semidirect
6. #11747003	C₂	semidirect
7. #11746997	C₂	semidirect
8. #11746991	C₂	semidirect
9. C₄×D₅×C₃⋊C₈	C₂	semidirect
10. #11746869	C₂	semidirect
11. #11746869	C₂	semidirect
90. #5024	D₅	semidirect
150. C₃×C₄×D₅	M₁₆	semidirect
153. C₃⋊#168	#41	semidirect
156. C₅×C₃⋊C₈	#41	semidirect
303. C₄×D₅	#208	semidirect
371. C₃⋊C₈	#713	semidirect
423. C₃×C₅	#2965	semidirect
479. C₅	#82517	semidirect
497. C₃	#10611669	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×#713	2
#11751125	2
C₅×#5024	2
#11747013	2
#11747010	2
#11747003	2
#11746997	2
#11746991	2
C₄×D₅×C₃⋊C₈	2
#11746869	2
#10611669	3
#82517	5